Lesson 4 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 4
Objective: Use attributes to identify and draw different quadrilaterals
including rectangles, rhombuses, parallelograms, and trapezoids.
Suggested Lesson Structure
Fluency Practice

Concept Development

Student Debrief

Total Time
(5 minutes)
(45 minutes)
(10 minutes)
(60 minutes)
Fluency Practice (5 minutes)
 Addition with Renaming 2.NBT.7
(5 minutes)
Addition with Renaming (5 minutes)
Materials: (S) Personal white board, hundreds place value chart (Lesson 3 Fluency Template)
Note: This fluency activity reviews the application of a chip model while recording with the algorithm. Allow
students work time between each problem, and reinforce place value understandings by having students say
their answers in both unit form and in standard form. Students use their personal white boards and a place
value chart to solve.
T:
T:
S:
T:
S:
T:
S:
Slide the place value chart template into your personal white board.
(Write 167 + 47 vertically on the board.) Let’s use a chip model to add. On your personal white
board, record your work using the algorithm.
(Solve.)
1 hundred 6 tens 7 ones plus 4 tens 7 ones is…?
2 hundreds 1 ten 4 ones!
167 + 47 is…?
214.
Continue with the following possible sequence: 285 + 38, 234 + 67, 317 + 94, and 367 + 55.
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
56
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 4 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM
Concept Development (45 minutes)
Materials: (T) Chart 2 from Lesson 1, index card, square tile, drawing of rhombus (S) 1 piece of 8½″ × 11″
white paper, centimeter rulers (Template), index card, highlighter
Note: Students need crayons or colored pencils for the homework.
Note: Today’s Application Problem has been omitted due to the time-intensive nature of the Concept
Development.
Note: The shape descriptions below provide a solid foundation to the definitions that are a part of students’
experience in later grades. Students are not expected to memorize these but rather to have an experience
drawing different quadrilaterals using the new attributes of square corners and parallel sides.
Quadrilateral: A four-sided polygon with four angles.
Trapezoid: A quadrilateral with at least one pair of parallel sides.
Parallelogram: A quadrilateral with two pairs of parallel sides.
Rectangle: A quadrilateral with four square corners.
Square: A special rectangle with sides that are all the same length.
Rhombus: A quadrilateral with four sides that are all the same length.
Distribute a piece of 8½″ × 11″ white paper, a centimeter ruler, and an index card to each
student. Instruct students to follow you as they fold their papers in half twice, such that they
have four sections on both sides of the paper for drawing. (See the image to the right.)
For precision, students should use a pencil so that they have the option to erase as they draw
the shapes.
Part 1: Drawing Square Corners and Parallel Lines
T:
S:
T:
T:
S:
T:
T:
S:
T:
Look at your index card. How many angles does it have?
Four!
Yes. Let’s look at our chart with other shapes that have four sides and
four angles. (Circle the shape on the chart with three acute angles, as
shown.)
How are the angles, or corners, on your index card different from
those of this shape?
The ones on my index card are all the same.  The corners on my card are in the shape of an L.
 The ones on the chart are big and small.
We call the angles on our index cards square corners.
Look at Chart 2 again. Student A, come up and circle a square corner.
(Uses a marker to identify and circle a square corner.)
Thumbs up if you agree. Let’s use our index card to check to see if Student A found
a square corner. (Put the corner of the index card in the corner of the shape, and
show students how to check by seeing if the lines of the shape line up with the
edges of the index card.)
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
57
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 4 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM
T:
T:
T:
Good job, Student A! This is a square corner. (Find and check other square corners.)
Let’s use our index cards as a tool to help us draw a quadrilateral with one square corner.
In one of the sections on your paper, draw a square corner using your index card as a guide.
Then, use the straightedge of your card to draw two more lines to complete your quadrilateral.
As time permits, students practice how to make other quadrilaterals.
T:
Place your centimeter ruler vertically in the next section on your paper. Use your centimeter ruler to
draw a straight line within the section.
S: (Draw a vertical line using a pencil.)
T: Without moving your ruler, use the opposite edge to draw a second
straight line of any length. (See the image to the right.)
S: (Draw a second straight line parallel to the first one using a pencil.)
T: What do you notice about these lines?
S: One is shorter than the other one.  They don’t
touch.  They don’t make a corner or an angle.
 They are the same distance apart. The lines never
come closer or get farther away from each other.
 They look like the sides of an H.
NOTES ON
T: If I used a really long ruler and a really long piece of
TRAPEZOIDS:
paper and kept drawing these lines, they would never
cross or touch.
According to the K–6 Geometry
Progressions, the term trapezoid may
T: We call these parallel lines. (Write parallel on the
have two different meanings,
board.) Look at the word parallel. The two L’s in the
depending on an exclusive or inclusive
middle of the word are parallel.
definition.
T: In the next section, position your ruler in different
 Exclusive: A trapezoid is a
ways—horizontally, diagonally—and practice making
quadrilateral with exactly one pair
more pairs of parallel lines.
of parallel sides.
S: (Practice making parallel lines with rulers in different
 Inclusive: A trapezoid is a
quadrilateral with at least one pair
positions.)
of parallel sides.
As time permits, direct students to Chart 2 again to answer the
While
both definitions are legitimate,
question, “Which of these shapes has a pair of parallel lines?”
Part 2: Drawing and Identifying a Trapezoid
T:
MP.6
S:
T:
S:
this curriculum uses the inclusive
definition. Therefore, a parallelogram
is also considered a trapezoid.
Position your ruler horizontally in a new section on
your paper. Use your ruler to draw a straight line that
is 8 cm long.
(Draw an 8 cm horizontal line using a pencil.)
Without moving your ruler, use the opposite edge of the ruler
to draw a second straight line. Then, with your ruler, join the
ends of both lines. (See the three examples shown to the
right.)
(Use rulers to join the ends of both lines, forming a trapezoid.)
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
58
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 4 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM
MP.6
T:
S:
T:
T:
S:
T:
S:
T:
S:
T:
S:
Part 3:
T:
S:
T:
S:
T:
S:
T:
S:
T:
S:
You made a four-sided polygon. What do we call it?
A quadrilateral!
Compare your quadrilateral with those of your neighbors.
Turn and talk: What new attribute do you notice about the sides of these quadrilaterals?
They all have parallel sides.  Two opposite sides are parallel, but on some of our shapes, the other
two aren’t.  The opposite sides are different lengths (or the same length, depending on the
figure).  They all have a pair of parallel sides.
Does this quadrilateral have at least one pair of parallel sides?
Yes!
(Point to a different trapezoid, which may be a parallelogram or rectangle.) How about this
quadrilateral?
Yes!
Your quadrilaterals are trapezoids if they have at least one pair of parallel sides. What is our new
word?
Trapezoid!
NOTES ON
Drawing and Identifying a Parallelogram
MULTIPLE MEANS
OF ENGAGEMENT:
Turn your paper over. In another section, use both
sides of your ruler to draw two parallel lines that are
Some students might have difficulty
drawing the different shapes. Support
each 8 cm long. Draw one line starting at zero and
their learning by providing them with a
stopping at 8 cm. Draw the other starting at any
template for their personal white
number but advancing 8 centimeters, like this.
boards that has some of the lines
(Demonstrate.) Now, it’s your turn.
already drawn so that all they have to
(Draw two parallel lines, each 8 cm in length.)
do is extend their drawings to connect
Use these parallel lines to make another quadrilateral
the sides. This is especially useful for
creating the trapezoid. Students may
by joining the ends of the parallel sides.
also be offered the use of a geoboard.
(Use a ruler to join the ends of both lines, forming a
parallelogram, as shown to the right.)
What do you notice about the connecting sides?
They are also parallel.
How can you be sure?
They look like they won’t touch if they keep going.  I can put my ruler down
that way and see that the other line runs along it without getting any closer.
Since this quadrilateral has two pairs of parallel sides (point to the parallel sides),
we call it a parallelogram. What’s it called?
A parallelogram!
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
59
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 4 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM
Part 4: Drawing and Identifying a Rectangle and Square and Relating the Rhombus to a Square
T:
S:
T:
S:
T:
S:
T:
S:
T:
T:
S:
T:
T:
S:
T:
S:
T:
T:
S:
T:
T:
Now, let’s draw another quadrilateral. In another section on your paper, use both sides of your ruler
to draw two parallel lines that are 8 cm long. This time, start both lines at zero on your ruler.
(Measure and draw two parallel lines, each beginning at zero and extending 8 cm in length.)
Complete the quadrilateral by drawing two more lines.
(Use a ruler to join the ends of both lines, forming a rectangle, as shown to the
right.)
Turn and talk: What do you notice about the angles of this special
quadrilateral?
They make square corners!
You already know this shape. What is it?
A rectangle!
Yes! A quadrilateral with four square corners is a
rectangle.
There is a special rectangle, too. It is special because it
has four square corners and four sides that are the
NOTES ON
same length. What do you think it is?
MULTIPLE MEANS
OF ACTION AND
A square!
EXPRESSION:
Watch as I draw a square. (Draw a square on the
Help
English
language learners practice
board.)
using the new geometric vocabulary.
Let’s double-check to see if it is a rectangle. Student B,
Make a game of it. Show students the
use your index card to check the corner angles to see if
shape, and ask them to say its name, or
they are all square corners.
ask them to match shapes with their
(Student B checks corners.) Yes! They are all square
names and say the names as they do.
corners.
Good. Finally, let’s check to see if the sides are all the
same length. Student C, use your ruler to measure
each side of the square.
(Student C measures sides.) All the sides are 10 cm! It is a square.
Just like a square, there is another quadrilateral that has four equal sides.
It looks like this. (Draw a rhombus on the board.)
What do you notice?
It looks like a square leaning over.  I don’t think it has square corners.
 I think the sides are all equal, like a square.  I see that both pairs of
opposite sides are parallel.
Yes! We call a quadrilateral with four equal sides a rhombus. It does have equal sides like a square,
but it doesn’t have to have square corners.
You’ve really flexed your geometry muscles today! On to the Problem Set!
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
60
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 4 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM
Problem Set (10 minutes)
Students should do their personal best to complete the
Problem Set within the allotted 10 minutes. For some
classes, it may be appropriate to modify the assignment by
specifying which problems they work on first. Some
problems do not specify a method for solving. Students
should solve these problems using the RDW approach
used for Application Problems.
Note: It is possible that there will not be enough time
today for the Problem Set. If just a few minutes remain,
consider having students instead draw different
quadrilaterals with the attributes of parallel lines and
square corners, and see if they can identify which names
apply to their shapes.
Student Debrief (10 minutes)
Lesson Objective: Use attributes to identify and draw
different quadrilaterals including rectangles, rhombuses,
parallelograms, and trapezoids.
The Student Debrief is intended to invite reflection and
active processing of the total lesson experience.
Invite students to review their solutions for the Problem
Set. They should check work by comparing answers
with a partner before going over answers as a class.
Look for misconceptions or misunderstandings that can
be addressed in the Debrief. Guide students in a
conversation to debrief the Problem Set and process
the lesson.
Any combination of the questions below may be used to
lead the discussion.



Turn and talk: What do you know about
parallel lines? Where do you see some in our
classroom?
Can a shape have different names? Tell your
partner other names that a quadrilateral can
be called.
Use your fingers to show your partner a square
corner. Use your fingers to show your partner
an angle that is not square.
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
61
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 4 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM



What did all the shapes we talked about today have in common? (They all were quadrilaterals, or
four-sided polygons, with four sides and four corners or angles.)
Use some of the new vocabulary words you learned today to describe to your partner the attributes
of a rectangle. A trapezoid. A parallelogram. A square. A rhombus.
What makes a square a special rectangle? Explain how you know.
Exit Ticket (3 minutes)
After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help with
assessing students’ understanding of the concepts that were presented in today’s lesson and planning more
effectively for future lessons. The questions may be read aloud to the students.
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
62
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 4 Problem Set 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Date
1. Use your ruler to draw 2 parallel lines that are not the same length.
2. Use your ruler to draw 2 parallel lines that are the same length.
3. Trace the parallel lines on each quadrilateral using a crayon. For each shape with
two sets of parallel lines, use two different colors. Use your index card to find
each square corner, and box it.
a.
b.
c.
d.
e.
f.
g.
h.
4. Draw a parallelogram with no square corners.
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
63
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 4 Problem Set 2 8
5. Draw a quadrilateral with 4 square corners.
6. Measure and label the sides of the figure to the right with
your centimeter ruler. What do you notice? Be ready to talk
about the attributes of this quadrilateral. Can you
remember what this polygon is called?
7. A square is a special rectangle. What makes it special?
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
64
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 4 Exit Ticket 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Date
Use crayons to trace the parallel sides on each quadrilateral. Use your index card to
find each square corner, and box it.
1.
2.
Lesson 4:
3.
4.
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
65
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
Lesson 4 Homework 2 8
Date
1. Use your ruler to draw 2 parallel lines that are not the same length.
2. Use your ruler to draw 2 parallel lines that are the same length.
3. Draw a quadrilateral with two sets of parallel sides. What is the name of this
quadrilateral?
4. Draw a quadrilateral with 4 square corners and opposite sides the same length.
What is the name of this quadrilateral?
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
66
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 4 Homework 2 8
5. A square is a special rectangle. What makes it special?
6. Color each quadrilateral with 4 square corners and two sets of parallel sides red.
Color each quadrilateral with no square corners and no parallel sides blue.
Circle each quadrilateral with one or more sets of parallel sides green.
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
67
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 4 Template 2 8
NYS COMMON CORE MATHEMATICS CURRICULUM
Copy onto heavy tag board and cut.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
2
3
4
5
6
7
8
9
10
11
12
13
14
15
cm c
cm
cm
cm
cm
cm
cm
1
cm

centimeter rulers
Lesson 4:
Use attributes to identify and draw different quadrilaterals including
rectangles, rhombuses, parallelograms, and trapezoids.
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 -Great Minds. eureka math.org
This file derived from G2-M8-TE-1.3.0-06.2015
68
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.